Characterization results for modal logics below first order identifies them as a fragment of first order logic. These results are very important to analyze the expressive power of a given logic. The first work in this direction was done by van Benthem [12] who used bisimulations to characterize the basic modal logic as the bisimulation invariant fragment of first order logic. There exists a hug...

A sequent calculus for hybrid logics is developed from a calculus for classical predicate logic by a series of transformations. We formalize the semantic theory of hybrid logic using a sequent calculus for predicate logic plus axioms. This works, but it is ugly. The unattractive features are removed one-by-one, until the final vestiges of the metalanguage can be set aside to reveal a fully inte...

A sequent calculus for hybrid logics is developed from a calculus for classical predicat logic by a series of transformations. We formalize the semantic theory of hybrid logic using a sequent calculus for predicate logic plus axioms. This works, but it is ugly. The unnattractive features are removed one-by-one, until the final vestiges of the metalanguage can be set aside to reveal a fully inte...

Unification modulo equational theories was originally introduced in automated deduction and term rewriting, but has recently also found applications in modal logics and description logics. In this talk, we review problems and results for unification in description logics, and relate them to equational unification and unification in modal logics. Related problems, like disunification, rigid E-un...

In this paper we present a generalization of belief functions over fuzzy events. In particular we focus on belief functions defined in the algebraic framework of finite MV-algebras of fuzzy sets. We introduce a fuzzy modal logic to formalize reasoning with belief functions on many-valued events. We prove, among other results, that several different notions of belief functions can be characteriz...